The present application describes systems and techniques relating to determining scalar quantizers for a signal, for example, determining scalar quantizers to generate an image of a desired distortion in wavelet-based compression.
Quantization is a process by which an input signal is limited to a set of discrete values that reduce the precision of the signal. Scalar quantization of digital signals, such as digital images, is used in various lossy data compression schemes, including the Joint Photographic Experts Group (JPEG) 2000 Recommendation|International Standard. In transform based lossy image compression systems, such as a JPEG 2000 system, the extent of compression is typically controlled by providing the compression system with a target, either a net compressed file size or an indication of how much loss of image quality is acceptable. For example, at the user interface level, an image quality indication can be input as a quality number of 1-10 or as a qualitative description (‘low quality’, ‘medium quality’, or ‘high quality’). In order to maintain consistency across images, the subjective quality inputs can be mapped to objective estimates of image distortion, such as peak-signal-to-noise-ratio (PSNR).
In the context of wavelet-based compression, such as in JPEG 2000, a desired PSNR can be achieved using a post-compression rate-distortion (PCRD) optimization. The PCRD method is a complex algorithm that operates on a wavelet-transformed and compressed image, assembling a smaller bitstream from the original compressed bitstream such that the new bitstream is optimal with respect to image distortion. In JPEG 2000, image compression can involve application of a discrete wavelet transform (DWT) to produce image transform coefficients, quantization of the transform coefficients, and entropy coding of the quantized coefficients. Valid JPEG 2000 codestreams can also be created without applying PCRD.